Pre-Algebra: like terms and the distributive property · Classroom

1. Hook

How to do this lesson online

Read (or listen to) what you’re learning. Don’t jump to the quiz.
Walk the worked example. Then use the interactive lab on this page.
Guided set → independent set → mastery check → teach-back.
If you write a paper, stay on campus: Citation Helper, Source Library, Paper Studio.

This is self-paced homeschool on Life Academy. Everything you need is on this page.

Today's puzzle

3(2x − 4) + 5x − 2: can you make this shorter without changing its value?

Then: lab → guided → quiz → teach it back. The lab is the lesson, not a decoration.

2. Teach

What you're learning

Simplify expressions using the distributive property and combining like terms, including negatives (CCSS 7.EE.A.1, 8.EE.C.7b).

Standards alignment: CCSS.MATH.CONTENT.8.EE (domain-level; works with any state’s standards)

STEM in this lesson

The distributive property explains area models and mental math: 7 × 102 = 7 × 100 + 7 × 2. Like terms let you simplify formulas.

Hold onto these

Distribute to every term in the parentheses, including the sign: −2(x − 5) = −2x + 10.
Like terms have identical variable parts; combine their coefficients.
Subtracting a group means distributing −1: 7 − (x + 3) = 4 − x.

This week’s lesson

3(2x − 4) + 5x − 2 = 6x − 12 + 5x − 2 = 11x − 14.

4(a − 2) − 3(a + 1) = 4a − 8 − 3a − 3 = a − 11.

Watch one worked example

Simplify 5 − 2(3y − 4) + y.
Distribute −2: 5 − 6y + 8 + y.
Combine: −5y + 13.
Test y = 1: 5 − 2(−1) + 1 = 8 and −5 + 13 = 8 ✓.

Now you try — with me

Simplify 2(4m + 1) − 3(m − 6) and −(2k − 7) + 4k. Test each with a value.

The usual mistake

Distributing the number but not the negative sign to the second term.

Why this shows up in real life

Simplifying is the first step in solving nearly every algebra equation.

No classroom teacher today — this page is the lesson. Follow the how-to, then the lab, then the quiz. Follow Lesson Studio, then the lab, then the quiz.

Interactive lab (on this page)

Change one variable. Record what happened. This model is the lab — not an off-site sim.

Your work — type it here

Type the answer. Then tap Check my work. This is the assignment — not optional reading.

1. 2(4m + 1) − 3(m − 6) when m = 1

2. −(2k − 7) + 4k when k = 3

3. 5 − 2(3y − 4) + y when y = 2

3. Guided practice

Try these with me — type the missing word, then check.

3(2x − 4) + 5x − 2 when x = 2

4(a − 2) − 3(a + 1) when a = 0

−2(x − 5) when x = 0

Reveal the thinking

Distribute (watch the signs), group like terms, combine, test a value.

4. Independent practice

Work the set. Check when finished — this is practice (mastery quiz is next).

5. Mastery check

Scored quiz — results save to your gradebook.

Show the math — don't only tap a letter

The lab is the worked example you can move. Then the quiz checks that you own Like terms and the distributive property (Algebra I start).

Math lab on this pageCount, group, shade, or rewrite — interactive, on Life Academy.Thinking CoachSocratic hints on this site. It will not take the quiz for you.Mastery checkScored quiz — results save to the gradebook on this device.

Classroom · Gradebook · Transcripts

Stay on this page. The studio, the lab, pictures, and Your work are the lesson.

6. Reflection / teach-back

Teach-back: Explain Like terms and the distributive property (Algebra I start) in your own words. Give one example and name the usual mistake.

Your teach-back